Constraining proton lifetime in SO(10) with stabilized doublet-triplet splitting

We present a class of realistic unified models based on supersymmetric SO(10) wherein issues related to natural doublet-triplet (DT) splitting are fully resolved. Using a minimal set of low dimensional Higgs fields which includes a single adjoint, we show that the Dimopoulos-Wilzcek mechanism for DT splitting can be made stable in the presence of all higher order operators without having pseudo-Goldstone bosons and flat directions. The μ term of order TeV is found to be naturally induced. A Z2-assisted anomalous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{U}{(1)_A} $\end{document} gauge symmetry plays a crucial role in achieving these results. The threshold corrections to α3(MZ), somewhat surprisingly, are found to be controlled by only a few effective parameters. This leads to a very predictive scenario for proton decay. As a novel feature, we find an interesting correlation between the d = 6 (p → e+π0) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ d = 5\left( {p \to \bar{\nu }{K^{+} }} \right) $\end{document} decay amplitudes which allows us to derive a constrained upper limit on the inverse rate of the e+π0 mode. Our results show that both modes should be observed with an improvement in the current sensitivity by about a factor of five to ten.